Date of Award
Summer 2023
Document Type
Open Access Dissertation
Department
Statistics
First Advisor
James W. Hardin
Abstract
This dissertation focuses on theory and application of discrete data methods, particularly approaches to over- and underdispersion relative to the Poisson distribution and an application of random forest and logistic regression modeling. The first chapter derives a score test for over- and underdispersion in the heaped generalized Poisson distribution. Equi-, over-, and underdispersed heaped generalized Poisson and heaped negative binomial data are simulated to evaluate the performance of the score test by comparing the power it achieves to that of Wald and likelihood ratio tests. We find that the score test we derive performs comparably to both the Wald and likelihood ratio tests. The second chapter explores the application and limitations of a model for the dispersion parameter in the double Poisson distribution utilizing a logistic-like link function. Data are simulated under various dispersion structures and a set of models assuming different maximum dispersion values are estimated for each. Through the simulation and a case study, we assess the application of the proposed model and identify potential improvements to aid in its effective utilization. Finally, the third chapter evaluates the performance of, and identifies important items in, a screening and a diagnostic tool for tic disorders in children. We also compare their results in terms of their ability to correctly predict tics in children and determine that the random forest models are more effective at reducing Type II errors.
Rights
© 2023, Rebecca C. Wardrop
Recommended Citation
Wardrop, R. C.(2023). Approaches to Detecting and Modeling Over-and Underdispersion in Alternative Count Data Distributions and an Application of Logistic Regression and Random Forest Modeling to Improve Screening Tools for Tic Disorders in Children. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/7425